A camera can record red, green and blue (RGB) responses/values, which depend on a sensor of the camera. In this manner, different cameras can produce different RGB responses for the same scene. Moreover, the RGB responses do not correspond to device-independent tristimulus values as defined by the Commission Internationale de l'Eclairage (CIE—the International Commission on Illumination), e.g., XYZ, standard RGB (sRGB), YCrCb, or the like. Further, the RGB responses for a given camera may be biased by an illuminant color, e.g., yellow light, blue light, white light, or the like. However, RGB values of an image can be mapped to target color values using a 3×3 color-transform. The target color values can be XYZs, sRGBs, etc., or camera RGBs for a specified illumination color (e.g., white light). Such mapping that uses the 3×3 color-transform is independent of camera exposure and brightness of the scene. This mapping, however, may provide inaccurate color correction over some portions of the RGB color-space where a 3×3 color-transform works less well.
An alternative mapping for color correction uses an n-term polynomial expansion of the RGB values (with n>3) and a corresponding 3×n color-transform. Here, the RGB values at each pixel of an image are expanded by n polynomial terms. For example, an RGB polynomial up to second order is represented as a 9-vector (R, G, B, R2, G2, B2, RG, RB, GB). With respect to this polynomial expansion, color correction of an image is a 9×3 color-transform that maps the expanded RGB values represented by the 9-vector to a 3-vector of XYZ values, for instance. For a given calibration set-up, a 3×9 color-transform corresponding to the 2nd order polynomial expansion can reduce colorimetric error by more than 50% relative to the 3×3 linear transform. However, unlike the 3×3 color-transform, a 3×n color-transform based on the polynomial expansion depends on exposure/brightness. For example, exposure/brightness changes of the RGB responses cause nonlinear changes of the polynomial expansion terms.